Reading List for Aspiring Mathematicians

May 8, 2021

My first college major was neuroscience. I learned about the beauty of mathematics by chance conversations, and eventually decided I deserved to give myself a chance to explore it. When I decided to switch my major to Honours Mathematics, I felt behind my peers who chose math as their major because they had been good at it growing up. After three years in graduate school, I have made my own contributions to mathematics and been invited to various places to present my work to the mathematical community. Although I still struggle with mathematics (as all mathematicians do), I no longer feel the same sense of insecurity that plagued me as an undergrad.

Here are a few of the readings I found useful, especially at the start of my mathematical journey. Also included are a few pieces of writing I found later on I wish I had the chance to read at a younger age. I hope this can be useful to the person who admires mathematicians but does not identify as a “math person”. I fully believe that, if you choose, you can become not only a “math person”, but a full-fledged mathematician.

Readings that helped me really understand math

Note: none of these were part of my undergraduate curriculum, but extra resources I found which helped me bridge the gap between what my program implicitly assumed I should already know and what I actually knew as an incoming student of mathematics.

Better Explained - this is the website which allowed me to truly understand how math was about concepts, not memorisation. It was especially enjoyable for me to re-learn some key concepts in trigonometry and functions and finally understand what they were about.

Gilbert Strang’s Calculus Book - I took Calculus I, II, and III without really understanding much. I had memorised how to do the problems and gotten disappointing grades in exchange. When I decided to major in math, I decided this wouldn’t do and took it upon myself to relearn the whole course sequence, focusing on the ideas rather than the computations.

A Book of Abstract Algebra by Charles Pinter - this was my first exposure to pure math and formal proofs. I found it illuminating to really attempt the exercises before checking the solutions. My approaches were embarrassingly wrong at first! It felt bad, but really taking the time to understand why I had been so wrong and why the solutions were right opened up the world of pure mathematics to me. To this day, coming up with a proof is the greatest joy of my life.

Readings that nourished my soul

A Mathematician’s Lament by Paul Lockart - an essay dissecting of how mathematics is misrepresented in pre-college education.

Mathematics for Human Flourishing by Francis Su - an essay discussing who is mathematics for and what can we gain by learning mathematics.

On Proof and Progress in Mathematics by William Thurston - an essay by one of the greats of mathematics about what mathematical progress is.

Peak by Anders Ericsson - a book dispelling the myth of born geniuses in various fields, including mathematics.

Popular readings which propagate harmful ideas

A Mathematician’s Apology by GH Hardy

Further Readings

A list of mathematical microaggressions by Francis Su - math students may recognise some, if not all, of the things listed. I believe it’s important to shift the focus away from how students should inherently feel already confident and competent in their mathematical abilitiesThey are students to develop their abilities, after all. Moreover, this kind of assumption disproportionally affects the marginalized, who may have already internalized messages that mathematics is not for them. I know I had. and put some of the burden onto the instructors, who are after all an integrate part of a student’s development.Unfortunately, not all instructors are as mindful as Francis Su, and despite what is said in the article I have known some who would purposefully use these sorts of microaggressions to gatekeep students under the veil of plausible deniability; it may be useful to desconstruct what exactly they are doing that is harmful, so to at least learn what - and who - not to listen to.

A letter to students about why professors have unearned power by Piper H. This essay explains the systems that allows professors to have unearned power, and why you shouldn’t let them decide whether you belong.

Piper H’s PhD thesis - Piper H graduated from Princeton (widely seen as the top school for mathematics), where for their thesis they laid out her mathematical research in layman’s terms with great social commentary.

An apt description of most math environments

Last updated: 22-10-2021.